Level of Each node in a Tree from source node (using BFS)

Given a tree with v vertices, find the level of each node in a tree from the source node.

Examples:

Input :   

Output :  Node      Level
           0          0
           1          1
           2          1
           3          2
           4          2
           5          2
           6          2
           7          3

Explanation : 

Input:

Output :  Node      Level
           0          0
           1          1
           2          1
           3          2
           4          2
Explanation:

Approach:
BFS(Breadth-First Search) is a graph traversal technique where a node and its neighbours are visited first and then the neighbours of neighbours. In simple terms, it traverses level-wise from the source. First, it traverses level 1 nodes (direct neighbours of source node) and then level 2 nodes (neighbours of source node) and so on. The BFS can be used to determine the level of each node from a given source node.

Algorithm:

1. Create the tree, a queue to store the nodes and insert the root or starting node in the queue. Create an extra array level of size v (number of vertices) and create a visited array.
2. Run a loop while size of queue is greater than 0.
3. Mark the current node as visited.
4. Pop one node from the queue and insert its childrens (if present) and update the size of the inserted node as level[child] = level[node] + 1.
5. Print all the node and its level.

Implementation:

C++

// CPP Program to determine level of each node
// and print level
#include <bits/stdc++.h>
using namespace std;

// function to determine level of each node starting
// from x using BFS
void printLevels(vector<int> graph[], int V, int x)
{
    // array to store level of each node
    int level[V];
    bool marked[V];

    // create a queue
    queue<int> que;

    // enqueue element x
    que.push(x);

    // initialize level of source node to 0
    level[x] = 0;

    // marked it as visited
    marked[x] = true;

    // do until queue is empty
    while (!que.empty()) {

        // get the first element of queue
        x = que.front();

        // dequeue element
        que.pop();

        // traverse neighbors of node x
        for (int i = 0; i < graph[x].size(); i++) {
            // b is neighbor of node x
            int b = graph[x][i];

            // if b is not marked already
            if (!marked[b]) {

                // enqueue b in queue
                que.push(b);

                // level of b is level of x + 1
                level[b] = level[x] + 1;

                // mark b
                marked[b] = true;
            }
        }
    }

    // display all nodes and their levels
    cout << "Nodes"
         << "    "
         << "Level" << endl;
    for (int i = 0; i < V; i++)
        cout << " " << i << "   -->   " << level[i] << endl;
}

// Driver Code
int main()
{
    // adjacency graph for tree
    int V = 8;
    vector<int> graph[V];

    graph[0].push_back(1);
    graph[0].push_back(2);
    graph[1].push_back(3);
    graph[1].push_back(4);
    graph[1].push_back(5);
    graph[2].push_back(5);
    graph[2].push_back(6);
    graph[6].push_back(7);

    // call levels function with source as 0
    printLevels(graph, V, 0);

    return 0;
}

Java

// Java Program to determine level of each node
// and print level
import java.util.*;

class GFG {

    // function to determine level of each node starting
    // from x using BFS
    static void printLevels(Vector<Vector<Integer> > graph,
                            int V, int x)
    {
        // array to store level of each node
        int level[] = new int[V];
        boolean marked[] = new boolean[V];

        // create a queue
        Queue<Integer> que = new LinkedList<Integer>();

        // enqueue element x
        que.add(x);

        // initialize level of source node to 0
        level[x] = 0;

        // marked it as visited
        marked[x] = true;

        // do until queue is empty
        while (que.size() > 0) {

            // get the first element of queue
            x = que.peek();

            // dequeue element
            que.remove();

            // traverse neighbors of node x
            for (int i = 0; i < graph.get(x).size(); i++) {
                // b is neighbor of node x
                int b = graph.get(x).get(i);

                // if b is not marked already
                if (!marked[b]) {

                    // enqueue b in queue
                    que.add(b);

                    // level of b is level of x + 1
                    level[b] = level[x] + 1;

                    // mark b
                    marked[b] = true;
                }
            }
        }

        // display all nodes and their levels
        System.out.println("Nodes"
                           + " "
                           + "Level");
        for (int i = 0; i < V; i++)
            System.out.println(" " + i + " --> "
                               + level[i]);
    }

    // Driver Code
    public static void main(String args[])
    {
        // adjacency graph for tree
        int V = 8;
        Vector<Vector<Integer> > graph
            = new Vector<Vector<Integer> >();

        for (int i = 0; i < V + 1; i++)
            graph.add(new Vector<Integer>());

        graph.get(0).add(1);
        graph.get(0).add(2);
        graph.get(1).add(3);
        graph.get(1).add(4);
        graph.get(1).add(5);
        graph.get(2).add(5);
        graph.get(2).add(6);
        graph.get(6).add(7);

        // call levels function with source as 0
        printLevels(graph, V, 0);
    }
}

// This code is contributed by Arnab Kundu

Python3

# Python3 Program to determine level
# of each node and print level
import queue

# function to determine level of
# each node starting from x using BFS


def printLevels(graph, V, x):

    # array to store level of each node
    level = [None] * V
    marked = [False] * V

    # create a queue
    que = queue.Queue()

    # enqueue element x
    que.put(x)

    # initialize level of source
    # node to 0
    level[x] = 0

    # marked it as visited
    marked[x] = True

    # do until queue is empty
    while (not que.empty()):

        # get the first element of queue
        x = que.get()

        # traverse neighbors of node x
        for i in range(len(graph[x])):

            # b is neighbor of node x
            b = graph[x][i]

            # if b is not marked already
            if (not marked[b]):

                # enqueue b in queue
                que.put(b)

                # level of b is level of x + 1
                level[b] = level[x] + 1

                # mark b
                marked[b] = True

    # display all nodes and their levels
    print("Nodes", " ", "Level")
    for i in range(V):
        print(" ", i,  " --> ", level[i])


# Driver Code
if __name__ == '__main__':

    # adjacency graph for tree
    V = 8
    graph = [[] for i in range(V)]

    graph[0].append(1)
    graph[0].append(2)
    graph[1].append(3)
    graph[1].append(4)
    graph[1].append(5)
    graph[2].append(5)
    graph[2].append(6)
    graph[6].append(7)

    # call levels function with source as 0
    printLevels(graph, V, 0)

# This code is contributed by PranchalK

C#

// C# Program to determine level of each node
// and print level
using System;
using System.Collections.Generic;

class GFG {

    // function to determine level of each node starting
    // from x using BFS
    static void printLevels(List<List<int> > graph, int V,
                            int x)
    {
        // array to store level of each node
        int[] level = new int[V];
        Boolean[] marked = new Boolean[V];

        // create a queue
        Queue<int> que = new Queue<int>();

        // enqueue element x
        que.Enqueue(x);

        // initialize level of source node to 0
        level[x] = 0;

        // marked it as visited
        marked[x] = true;

        // do until queue is empty
        while (que.Count > 0) {

            // get the first element of queue
            x = que.Peek();

            // dequeue element
            que.Dequeue();

            // traverse neighbors of node x
            for (int i = 0; i < graph[x].Count; i++) {
                // b is neighbor of node x
                int b = graph[x][i];

                // if b is not marked already
                if (!marked[b]) {

                    // enqueue b in queue
                    que.Enqueue(b);

                    // level of b is level of x + 1
                    level[b] = level[x] + 1;

                    // mark b
                    marked[b] = true;
                }
            }
        }

        // display all nodes and their levels
        Console.WriteLine("Nodes"
                          + " "
                          + "Level");
        for (int i = 0; i < V; i++)
            Console.WriteLine(" " + i + " --> " + level[i]);
    }

    // Driver Code
    public static void Main(String[] args)
    {
        // adjacency graph for tree
        int V = 8;
        List<List<int> > graph = new List<List<int> >();

        for (int i = 0; i < V + 1; i++)
            graph.Add(new List<int>());

        graph[0].Add(1);
        graph[0].Add(2);
        graph[1].Add(3);
        graph[1].Add(4);
        graph[1].Add(5);
        graph[2].Add(5);
        graph[2].Add(6);
        graph[6].Add(7);

        // call levels function with source as 0
        printLevels(graph, V, 0);
    }
}

// This code is contributed by Princi Singh

Javascript

<script>

// Javascript Program to determine level of each node
// and print level

// function to determine level of each node starting
// from x using BFS
function printLevels(graph, V, x)
{
    // array to store level of each node
    var level = Array(V);
    var marked = Array(V).fill(false);

    // create a queue
    var que = [];

    // enqueue element x
    que.push(x);

    // initialize level of source node to 0
    level[x] = 0;

    // marked it as visited
    marked[x] = true;

    // do until queue is empty
    while (que.length > 0)
    {

        // get the first element of queue
        x = que[0];

        // dequeue element
        que.shift();

        // traverse neighbors of node x
        for (var i = 0; i < graph[x].length; i++)
        {
            // b is neighbor of node x
            var b = graph[x][i];

            // if b is not marked already
            if (!marked[b])
            {

                // enqueue b in queue
                que.push(b);

                // level of b is level of x + 1
                level[b] = level[x] + 1;

                // mark b
                marked[b] = true;
            }
        }
    }

    // display all nodes and their levels
    document.write("Nodes" + " " + "Level<br>");
    for (var i = 0; i < V; i++)
        document.write(" " + i +" --> " + level[i]+"<br>");
}

// Driver Code
// adjacency graph for tree
var V = 8;
var graph = Array.from(Array(V+1), ()=>Array());

graph[0].push(1);
graph[0].push(2);
graph[1].push(3);
graph[1].push(4);
graph[1].push(5);
graph[2].push(5);
graph[2].push(6);
graph[6].push(7);
// call levels function with source as 0
printLevels(graph, V, 0);

// This code is contributed by importantly.

</script>

Output

Nodes    Level
 0   -->   0
 1   -->   1
 2   -->   1
 3   -->   2
 4   -->   2
 5   -->   2
 6   -->   2
 7   -->   3

Complexity Analysis:

• Time Complexity: O(n). 
  In BFS traversal every node is visited only once, so Time Complexity is O(n).
• Space Complexity: O(n). 
  The space is required to store the nodes in a queue.